Index: Demo/classes/Rat.py =================================================================== --- Demo/classes/Rat.py (revision 59867) +++ Demo/classes/Rat.py (working copy) @@ -1,310 +0,0 @@ -'''\ -This module implements rational numbers. - -The entry point of this module is the function - rat(numerator, denominator) -If either numerator or denominator is of an integral or rational type, -the result is a rational number, else, the result is the simplest of -the types float and complex which can hold numerator/denominator. -If denominator is omitted, it defaults to 1. -Rational numbers can be used in calculations with any other numeric -type. The result of the calculation will be rational if possible. - -There is also a test function with calling sequence - test() -The documentation string of the test function contains the expected -output. -''' - -# Contributed by Sjoerd Mullender - -from types import * - -def gcd(a, b): - '''Calculate the Greatest Common Divisor.''' - while b: - a, b = b, a%b - return a - -def rat(num, den = 1): - # must check complex before float - if isinstance(num, complex) or isinstance(den, complex): - # numerator or denominator is complex: return a complex - return complex(num) / complex(den) - if isinstance(num, float) or isinstance(den, float): - # numerator or denominator is float: return a float - return float(num) / float(den) - # otherwise return a rational - return Rat(num, den) - -class Rat: - '''This class implements rational numbers.''' - - def __init__(self, num, den = 1): - if den == 0: - raise ZeroDivisionError, 'rat(x, 0)' - - # normalize - - # must check complex before float - if (isinstance(num, complex) or - isinstance(den, complex)): - # numerator or denominator is complex: - # normalized form has denominator == 1+0j - self.__num = complex(num) / complex(den) - self.__den = complex(1) - return - if isinstance(num, float) or isinstance(den, float): - # numerator or denominator is float: - # normalized form has denominator == 1.0 - self.__num = float(num) / float(den) - self.__den = 1.0 - return - if (isinstance(num, self.__class__) or - isinstance(den, self.__class__)): - # numerator or denominator is rational - new = num / den - if not isinstance(new, self.__class__): - self.__num = new - if isinstance(new, complex): - self.__den = complex(1) - else: - self.__den = 1.0 - else: - self.__num = new.__num - self.__den = new.__den - else: - # make sure numerator and denominator don't - # have common factors - # this also makes sure that denominator > 0 - g = gcd(num, den) - self.__num = num / g - self.__den = den / g - # try making numerator and denominator of IntType if they fit - try: - numi = int(self.__num) - deni = int(self.__den) - except (OverflowError, TypeError): - pass - else: - if self.__num == numi and self.__den == deni: - self.__num = numi - self.__den = deni - - def __repr__(self): - return 'Rat(%s,%s)' % (self.__num, self.__den) - - def __str__(self): - if self.__den == 1: - return str(self.__num) - else: - return '(%s/%s)' % (str(self.__num), str(self.__den)) - - # a + b - def __add__(a, b): - try: - return rat(a.__num * b.__den + b.__num * a.__den, - a.__den * b.__den) - except OverflowError: - return rat(long(a.__num) * long(b.__den) + - long(b.__num) * long(a.__den), - long(a.__den) * long(b.__den)) - - def __radd__(b, a): - return Rat(a) + b - - # a - b - def __sub__(a, b): - try: - return rat(a.__num * b.__den - b.__num * a.__den, - a.__den * b.__den) - except OverflowError: - return rat(long(a.__num) * long(b.__den) - - long(b.__num) * long(a.__den), - long(a.__den) * long(b.__den)) - - def __rsub__(b, a): - return Rat(a) - b - - # a * b - def __mul__(a, b): - try: - return rat(a.__num * b.__num, a.__den * b.__den) - except OverflowError: - return rat(long(a.__num) * long(b.__num), - long(a.__den) * long(b.__den)) - - def __rmul__(b, a): - return Rat(a) * b - - # a / b - def __div__(a, b): - try: - return rat(a.__num * b.__den, a.__den * b.__num) - except OverflowError: - return rat(long(a.__num) * long(b.__den), - long(a.__den) * long(b.__num)) - - def __rdiv__(b, a): - return Rat(a) / b - - # a % b - def __mod__(a, b): - div = a / b - try: - div = int(div) - except OverflowError: - div = long(div) - return a - b * div - - def __rmod__(b, a): - return Rat(a) % b - - # a ** b - def __pow__(a, b): - if b.__den != 1: - if isinstance(a.__num, complex): - a = complex(a) - else: - a = float(a) - if isinstance(b.__num, complex): - b = complex(b) - else: - b = float(b) - return a ** b - try: - return rat(a.__num ** b.__num, a.__den ** b.__num) - except OverflowError: - return rat(long(a.__num) ** b.__num, - long(a.__den) ** b.__num) - - def __rpow__(b, a): - return Rat(a) ** b - - # -a - def __neg__(a): - try: - return rat(-a.__num, a.__den) - except OverflowError: - # a.__num == sys.maxint - return rat(-long(a.__num), a.__den) - - # abs(a) - def __abs__(a): - return rat(abs(a.__num), a.__den) - - # int(a) - def __int__(a): - return int(a.__num / a.__den) - - # long(a) - def __long__(a): - return long(a.__num) / long(a.__den) - - # float(a) - def __float__(a): - return float(a.__num) / float(a.__den) - - # complex(a) - def __complex__(a): - return complex(a.__num) / complex(a.__den) - - # cmp(a,b) - def __cmp__(a, b): - diff = Rat(a - b) - if diff.__num < 0: - return -1 - elif diff.__num > 0: - return 1 - else: - return 0 - - def __rcmp__(b, a): - return cmp(Rat(a), b) - - # a != 0 - def __nonzero__(a): - return a.__num != 0 - - # coercion - def __coerce__(a, b): - return a, Rat(b) - -def test(): - '''\ - Test function for rat module. - - The expected output is (module some differences in floating - precission): - -1 - -1 - 0 0L 0.1 (0.1+0j) - [Rat(1,2), Rat(-3,10), Rat(1,25), Rat(1,4)] - [Rat(-3,10), Rat(1,25), Rat(1,4), Rat(1,2)] - 0 - (11/10) - (11/10) - 1.1 - OK - 2 1.5 (3/2) (1.5+1.5j) (15707963/5000000) - 2 2 2.0 (2+0j) - - 4 0 4 1 4 0 - 3.5 0.5 3.0 1.33333333333 2.82842712475 1 - (7/2) (1/2) 3 (4/3) 2.82842712475 1 - (3.5+1.5j) (0.5-1.5j) (3+3j) (0.666666666667-0.666666666667j) (1.43248815986+2.43884761145j) 1 - 1.5 1 1.5 (1.5+0j) - - 3.5 -0.5 3.0 0.75 2.25 -1 - 3.0 0.0 2.25 1.0 1.83711730709 0 - 3.0 0.0 2.25 1.0 1.83711730709 1 - (3+1.5j) -1.5j (2.25+2.25j) (0.5-0.5j) (1.50768393746+1.04970907623j) -1 - (3/2) 1 1.5 (1.5+0j) - - (7/2) (-1/2) 3 (3/4) (9/4) -1 - 3.0 0.0 2.25 1.0 1.83711730709 -1 - 3 0 (9/4) 1 1.83711730709 0 - (3+1.5j) -1.5j (2.25+2.25j) (0.5-0.5j) (1.50768393746+1.04970907623j) -1 - (1.5+1.5j) (1.5+1.5j) - - (3.5+1.5j) (-0.5+1.5j) (3+3j) (0.75+0.75j) 4.5j -1 - (3+1.5j) 1.5j (2.25+2.25j) (1+1j) (1.18235814075+2.85446505899j) 1 - (3+1.5j) 1.5j (2.25+2.25j) (1+1j) (1.18235814075+2.85446505899j) 1 - (3+3j) 0j 4.5j (1+0j) (-0.638110484918+0.705394566962j) 0 - ''' - print rat(-1L, 1) - print rat(1, -1) - a = rat(1, 10) - print int(a), long(a), float(a), complex(a) - b = rat(2, 5) - l = [a+b, a-b, a*b, a/b] - print l - l.sort() - print l - print rat(0, 1) - print a+1 - print a+1L - print a+1.0 - try: - print rat(1, 0) - raise SystemError, 'should have been ZeroDivisionError' - except ZeroDivisionError: - print 'OK' - print rat(2), rat(1.5), rat(3, 2), rat(1.5+1.5j), rat(31415926,10000000) - list = [2, 1.5, rat(3,2), 1.5+1.5j] - for i in list: - print i, - if not isinstance(i, complex): - print int(i), float(i), - print complex(i) - print - for j in list: - print i + j, i - j, i * j, i / j, i ** j, - if not (isinstance(i, complex) or - isinstance(j, complex)): - print cmp(i, j) - print - - -if __name__ == '__main__': - test() Index: Lib/rational.py =================================================================== --- Lib/rational.py (revision 59671) +++ Lib/rational.py (working copy) @@ -1,310 +1,382 @@ -'''\ -This module implements rational numbers. +# Contributed by Sjoerd Mullender -The entry point of this module is the function - rat(numerator, denominator) -If either numerator or denominator is of an integral or rational type, -the result is a rational number, else, the result is the simplest of -the types float and complex which can hold numerator/denominator. -If denominator is omitted, it defaults to 1. -Rational numbers can be used in calculations with any other numeric -type. The result of the calculation will be rational if possible. +"""Rational, infinite-precision, real numbers.""" -There is also a test function with calling sequence - test() -The documentation string of the test function contains the expected -output. -''' +from __future__ import division +import math +import numbers +import operator -# Contributed by Sjoerd Mullender +__all__ = ["Rational"] -from types import * +RationalAbc = numbers.Rational -def gcd(a, b): - '''Calculate the Greatest Common Divisor.''' + +def _gcd(a, b): + """Calculate the Greatest Common Divisor. + + Unless b==0, the result will have the same sign as b (so that when + b is divided by it, the result comes out positive). + """ while b: a, b = b, a%b return a -def rat(num, den = 1): - # must check complex before float - if isinstance(num, complex) or isinstance(den, complex): - # numerator or denominator is complex: return a complex - return complex(num) / complex(den) - if isinstance(num, float) or isinstance(den, float): - # numerator or denominator is float: return a float - return float(num) / float(den) - # otherwise return a rational - return Rat(num, den) -class Rat: - '''This class implements rational numbers.''' +def _binary_float_to_ratio(x): + """x -> (top, bot), a pair of ints s.t. x = top/bot. - def __init__(self, num, den = 1): - if den == 0: - raise ZeroDivisionError, 'rat(x, 0)' + The conversion is done exactly, without rounding. + bot > 0 guaranteed. + Some form of binary fp is assumed. + Pass NaNs or infinities at your own risk. - # normalize + >>> _binary_float_to_ratio(10.0) + (10, 1) + >>> _binary_float_to_ratio(0.0) + (0, 1) + >>> _binary_float_to_ratio(-.25) + (-1, 4) + """ - # must check complex before float - if (isinstance(num, complex) or - isinstance(den, complex)): - # numerator or denominator is complex: - # normalized form has denominator == 1+0j - self.__num = complex(num) / complex(den) - self.__den = complex(1) - return - if isinstance(num, float) or isinstance(den, float): - # numerator or denominator is float: - # normalized form has denominator == 1.0 - self.__num = float(num) / float(den) - self.__den = 1.0 - return - if (isinstance(num, self.__class__) or - isinstance(den, self.__class__)): - # numerator or denominator is rational - new = num / den - if not isinstance(new, self.__class__): - self.__num = new - if isinstance(new, complex): - self.__den = complex(1) - else: - self.__den = 1.0 - else: - self.__num = new.__num - self.__den = new.__den + if x == 0: + return 0, 1 + f, e = math.frexp(x) + signbit = 1 + if f < 0: + f = -f + signbit = -1 + assert 0.5 <= f < 1.0 + # x = signbit * f * 2**e exactly + + # Suck up CHUNK bits at a time; 28 is enough so that we suck + # up all bits in 2 iterations for all known binary double- + # precision formats, and small enough to fit in an int. + CHUNK = 28 + top = 0L + # invariant: x = signbit * (top + f) * 2**e exactly + while f: + f = math.ldexp(f, CHUNK) + digit = trunc(f) + assert digit >> CHUNK == 0 + top = (top << CHUNK) | digit + f = f - digit + assert 0.0 <= f < 1.0 + e = e - CHUNK + assert top + + # Add in the sign bit. + top = signbit * top + + # now x = top * 2**e exactly; fold in 2**e + if e>0: + return (top * 2**e, 1) else: - # make sure numerator and denominator don't - # have common factors - # this also makes sure that denominator > 0 - g = gcd(num, den) - self.__num = num / g - self.__den = den / g - # try making numerator and denominator of IntType if they fit - try: - numi = int(self.__num) - deni = int(self.__den) - except (OverflowError, TypeError): - pass - else: - if self.__num == numi and self.__den == deni: - self.__num = numi - self.__den = deni + return (top, 2 ** -e) + +class Rational(RationalAbc): + """This class implements rational numbers. + + Rational(8, 6) will produce a rational number equivalent to + 4/3. Both arguments must be convertible to ints. The denominator + defaults to 1 so that Rational(3) == 3. + + """ + + __slots__ = ('_numerator', '_denominator') + + def __init__(self, numerator, denominator=1): + if (not isinstance(numerator, numbers.Integral) or + not isinstance(denominator, numbers.Integral)): + raise TypeError("Rational(%(numerator)s, %(denominator)s):" + " Both arguments must be integral." % locals()) + + if denominator == 0: + raise ZeroDivisionError('Rational(%s, 0)' % numerator) + + g = _gcd(numerator, denominator) + self._numerator = int(numerator // g) + self._denominator = int(denominator // g) + + @classmethod + def from_float(cls, f): + """Converts a float to a rational number, exactly.""" + if not isinstance(f, float): + raise TypeError("%s.from_float() only takes floats, not %r (%s)" % + (cls.__name__, f, type(f).__name__)) + if math.isnan(f) or math.isinf(f): + # Actually, they can be represented as (0,0), (-1,0), and + # (1, 0). XXX: Do we want to? + raise TypeError("Cannot convert %r to %s." % (f, cls.__name__)) + return cls(*_binary_float_to_ratio(f)) + + @property + def numerator(a): + return a._numerator + + @property + def denominator(a): + return a._denominator + def __repr__(self): - return 'Rat(%s,%s)' % (self.__num, self.__den) + """repr(self)""" + return ('rational.Rational(%r,%r)' % + (self.numerator, self.denominator)) def __str__(self): - if self.__den == 1: - return str(self.__num) + """str(self)""" + if self.denominator == 1: + return str(self.numerator) else: - return '(%s/%s)' % (str(self.__num), str(self.__den)) + return '(%s/%s)' % (self.numerator, self.denominator) - # a + b - def __add__(a, b): - try: - return rat(a.__num * b.__den + b.__num * a.__den, - a.__den * b.__den) - except OverflowError: - return rat(long(a.__num) * long(b.__den) + - long(b.__num) * long(a.__den), - long(a.__den) * long(b.__den)) + def _operator_fallbacks(monomorphic_operator, fallback_operator): + """Generates forward and reverse operators given a purely-rational + operator and a function from the operator module. - def __radd__(b, a): - return Rat(a) + b + Use this like: + __op__, __rop__ = _operator_fallbacks(just_rational_op, operator.op) - # a - b - def __sub__(a, b): - try: - return rat(a.__num * b.__den - b.__num * a.__den, - a.__den * b.__den) - except OverflowError: - return rat(long(a.__num) * long(b.__den) - - long(b.__num) * long(a.__den), - long(a.__den) * long(b.__den)) + """ + def forward(a, b): + if isinstance(b, RationalAbc): + # Includes ints. + return monomorphic_operator(a, b) + elif isinstance(b, float): + return fallback_operator(float(a), b) + elif isinstance(b, complex): + return fallback_operator(complex(a), b) + else: + return NotImplemented + forward.__name__ = '__' + fallback_operator.__name__ + '__' + forward.__doc__ = monomorphic_operator.__doc__ - def __rsub__(b, a): - return Rat(a) - b + def reverse(b, a): + if isinstance(a, RationalAbc): + # Includes ints. + return monomorphic_operator(a, b) + elif isinstance(a, numbers.Real): + return fallback_operator(float(a), float(b)) + elif isinstance(a, numbers.Complex): + return fallback_operator(complex(a), complex(b)) + else: + return NotImplemented + reverse.__name__ = '__r' + fallback_operator.__name__ + '__' + reverse.__doc__ = monomorphic_operator.__doc__ - # a * b - def __mul__(a, b): - try: - return rat(a.__num * b.__num, a.__den * b.__den) - except OverflowError: - return rat(long(a.__num) * long(b.__num), - long(a.__den) * long(b.__den)) + return forward, reverse - def __rmul__(b, a): - return Rat(a) * b + def _add(a, b): + """a + b""" + return Rational(a.numerator * b.denominator + + b.numerator * a.denominator, + a.denominator * b.denominator) - # a / b - def __div__(a, b): - try: - return rat(a.__num * b.__den, a.__den * b.__num) - except OverflowError: - return rat(long(a.__num) * long(b.__den), - long(a.__den) * long(b.__num)) + __add__, __radd__ = _operator_fallbacks(_add, operator.add) - def __rdiv__(b, a): - return Rat(a) / b + def _sub(a, b): + """a - b""" + return Rational(a.numerator * b.denominator - + b.numerator * a.denominator, + a.denominator * b.denominator) - # a % b - def __mod__(a, b): + __sub__, __rsub__ = _operator_fallbacks(_sub, operator.sub) + + def _mul(a, b): + """a * b""" + return Rational(a.numerator * b.numerator, a.denominator * b.denominator) + + __mul__, __rmul__ = _operator_fallbacks(_mul, operator.mul) + + def _div(a, b): + """a / b""" + return Rational(a.numerator * b.denominator, + a.denominator * b.numerator) + + __truediv__, __rtruediv__ = _operator_fallbacks(_div, operator.truediv) + __div__, __rdiv__ = _operator_fallbacks(_div, operator.div) + + @classmethod + def _floordiv(cls, a, b): div = a / b - try: - div = int(div) - except OverflowError: - div = long(div) + if isinstance(div, RationalAbc): + # trunc(math.floor(div)) doesn't work if the rational is + # more precise than a float because the intermediate + # rounding may cross an integer boundary. + return div.numerator // div.denominator + else: + return math.floor(div) + + def __floordiv__(a, b): + """a // b""" + # Will be math.floor(a / b) in 3.0. + return a._floordiv(a, b) + + def __rfloordiv__(b, a): + """a // b""" + # Will be math.floor(a / b) in 3.0. + return b._floordiv(a, b) + + @classmethod + def _mod(cls, a, b): + div = a // b return a - b * div + + def __mod__(a, b): + """a % b""" + return a._mod(a, b) def __rmod__(b, a): - return Rat(a) % b + """a % b""" + return b._mod(a, b) - # a ** b def __pow__(a, b): - if b.__den != 1: - if isinstance(a.__num, complex): - a = complex(a) + """a ** b + + If b is not an integer, the result will be a float or complex + since roots are generally irrational. If b is an integer, the + result will be rational. + + """ + if isinstance(b, RationalAbc): + if b.denominator == 1: + power = b.numerator + if power >= 0: + return Rational(a.numerator ** power, + a.denominator ** power) + else: + return Rational(a.denominator ** -power, + a.numerator ** -power) else: - a = float(a) - if isinstance(b.__num, complex): - b = complex(b) - else: - b = float(b) - return a ** b - try: - return rat(a.__num ** b.__num, a.__den ** b.__num) - except OverflowError: - return rat(long(a.__num) ** b.__num, - long(a.__den) ** b.__num) + # A fractional power will generally produce an + # irrational number. + return float(a) ** float(b) + else: + return float(a) ** b def __rpow__(b, a): - return Rat(a) ** b + """a ** b""" + if b.denominator == 1 and b.numerator >= 0: + # If a is an int, keep it that way if possible. + return a ** b.numerator - # -a + if isinstance(a, RationalAbc): + return Rational(a.numerator, a.denominator) ** b + + if b.denominator == 1: + return a ** b.numerator + + return a ** float(b) + def __neg__(a): - try: - return rat(-a.__num, a.__den) - except OverflowError: - # a.__num == sys.maxint - return rat(-long(a.__num), a.__den) + """-a""" + return Rational(-a.numerator, a.denominator) - # abs(a) def __abs__(a): - return rat(abs(a.__num), a.__den) + """abs(a)""" + return Rational(abs(a.numerator), a.denominator) - # int(a) - def __int__(a): - return int(a.__num / a.__den) + def __trunc__(a): + """trunc(a)""" + if a.numerator < 0: + return -(-a.numerator // a.denominator) + else: + return a.numerator // a.denominator - # long(a) - def __long__(a): - return long(a.__num) / long(a.__den) + def __floor__(a): + """Will be math.floor(a) in 3.0.""" + return a.numerator // a.denominator - # float(a) - def __float__(a): - return float(a.__num) / float(a.__den) + def __ceil__(a): + """Will be math.ceil(a) in 3.0.""" + # The negations cleverly convince floordiv to return the ceiling. + return -(-a.numerator // a.denominator) - # complex(a) - def __complex__(a): - return complex(a.__num) / complex(a.__den) + def __round__(self, ndigits=None): + """Will be round(self, ndigits) in 3.0. - # cmp(a,b) - def __cmp__(a, b): - diff = Rat(a - b) - if diff.__num < 0: - return -1 - elif diff.__num > 0: - return 1 + Rounds half toward even. + """ + if ndigits is None: + floor, remainder = divmod(self.numerator, self.denominator) + if remainder * 2 < self.denominator: + return floor + elif remainder * 2 > self.denominator: + return floor + 1 + # Deal with the half case: + elif floor % 2 == 0: + return floor + else: + return floor + 1 + shift = 10**abs(ndigits) + # See _operator_fallbacks.forward to check that the results of + # these operations will always be Rational and therefore have + # __round__(). + if ndigits > 0: + return Rational((self * shift).__round__(), shift) else: - return 0 + return Rational((self / shift).__round__() * shift) - def __rcmp__(b, a): - return cmp(Rat(a), b) + def __hash__(self): + """hash(self) - # a != 0 - def __nonzero__(a): - return a.__num != 0 + Tricky because values that are exactly representable as a + float must have the same hash as that float. - # coercion - def __coerce__(a, b): - return a, Rat(b) + """ + # Expensive check, but definitely correct. + if self == float(self): + return hash(float(self)) + else: + # This algorithm will make simple fractions collide often. :-( + return hash(self.numerator) ^ hash(self.denominator) -def test(): - '''\ - Test function for rat module. + def __eq__(a, b): + """a == b""" + if isinstance(b, RationalAbc): + return (a.numerator == b.numerator and + a.denominator == b.denominator) + elif isinstance(b, float): + return a == a.from_float(b) + else: + return float(a) == b + + def _subtractAndCompareToZero(a, b, op): + """Helper function for comparison operators. - The expected output is (module some differences in floating - precission): - -1 - -1 - 0 0L 0.1 (0.1+0j) - [Rat(1,2), Rat(-3,10), Rat(1,25), Rat(1,4)] - [Rat(-3,10), Rat(1,25), Rat(1,4), Rat(1,2)] - 0 - (11/10) - (11/10) - 1.1 - OK - 2 1.5 (3/2) (1.5+1.5j) (15707963/5000000) - 2 2 2.0 (2+0j) + Subtracts b from a, exactly if possible, and compares the + result with 0 using op, in such a way that the comparison + won't recurse. If the difference is NotImplemented, returns + that instead. - 4 0 4 1 4 0 - 3.5 0.5 3.0 1.33333333333 2.82842712475 1 - (7/2) (1/2) 3 (4/3) 2.82842712475 1 - (3.5+1.5j) (0.5-1.5j) (3+3j) (0.666666666667-0.666666666667j) (1.43248815986+2.43884761145j) 1 - 1.5 1 1.5 (1.5+0j) + """ + if isinstance(b, float): + b = a.from_float(b) + diff = a - b + if diff is NotImplemented: + return diff + elif isinstance(diff, RationalAbc): + return op(diff.numerator, 0) + else: + return op(diff, 0) + + def __lt__(a, b): + """a < b""" + return a._subtractAndCompareToZero(b, operator.lt) - 3.5 -0.5 3.0 0.75 2.25 -1 - 3.0 0.0 2.25 1.0 1.83711730709 0 - 3.0 0.0 2.25 1.0 1.83711730709 1 - (3+1.5j) -1.5j (2.25+2.25j) (0.5-0.5j) (1.50768393746+1.04970907623j) -1 - (3/2) 1 1.5 (1.5+0j) + def __gt__(a, b): + """a > b""" + return a._subtractAndCompareToZero(b, operator.gt) - (7/2) (-1/2) 3 (3/4) (9/4) -1 - 3.0 0.0 2.25 1.0 1.83711730709 -1 - 3 0 (9/4) 1 1.83711730709 0 - (3+1.5j) -1.5j (2.25+2.25j) (0.5-0.5j) (1.50768393746+1.04970907623j) -1 - (1.5+1.5j) (1.5+1.5j) + def __le__(a, b): + """a <= b""" + return a._subtractAndCompareToZero(b, operator.le) - (3.5+1.5j) (-0.5+1.5j) (3+3j) (0.75+0.75j) 4.5j -1 - (3+1.5j) 1.5j (2.25+2.25j) (1+1j) (1.18235814075+2.85446505899j) 1 - (3+1.5j) 1.5j (2.25+2.25j) (1+1j) (1.18235814075+2.85446505899j) 1 - (3+3j) 0j 4.5j (1+0j) (-0.638110484918+0.705394566962j) 0 - ''' - print rat(-1L, 1) - print rat(1, -1) - a = rat(1, 10) - print int(a), long(a), float(a), complex(a) - b = rat(2, 5) - l = [a+b, a-b, a*b, a/b] - print l - l.sort() - print l - print rat(0, 1) - print a+1 - print a+1L - print a+1.0 - try: - print rat(1, 0) - raise SystemError, 'should have been ZeroDivisionError' - except ZeroDivisionError: - print 'OK' - print rat(2), rat(1.5), rat(3, 2), rat(1.5+1.5j), rat(31415926,10000000) - list = [2, 1.5, rat(3,2), 1.5+1.5j] - for i in list: - print i, - if not isinstance(i, complex): - print int(i), float(i), - print complex(i) - print - for j in list: - print i + j, i - j, i * j, i / j, i ** j, - if not (isinstance(i, complex) or - isinstance(j, complex)): - print cmp(i, j) - print + def __ge__(a, b): + """a >= b""" + return a._subtractAndCompareToZero(b, operator.ge) - -if __name__ == '__main__': - test() + def __nonzero__(a): + """a != 0""" + return a.numerator != 0 Index: Lib/numbers.py =================================================================== --- Lib/numbers.py (revision 59867) +++ Lib/numbers.py (working copy) @@ -5,6 +5,7 @@ TODO: Fill out more detailed documentation on the operators.""" +from __future__ import division from abc import ABCMeta, abstractmethod, abstractproperty __all__ = ["Number", "Exact", "Inexact", @@ -63,7 +64,8 @@ def __complex__(self): """Return a builtin complex instance. Called for complex(self).""" - def __bool__(self): + # Will be __bool__ in 3.0. + def __nonzero__(self): """True if self != 0. Called for bool(self).""" return self != 0 @@ -122,15 +124,31 @@ @abstractmethod def __div__(self, other): - """self / other; should promote to float or complex when necessary.""" + """self / other without __future__ division + + May promote to float. + """ raise NotImplementedError @abstractmethod def __rdiv__(self, other): - """other / self""" + """other / self without __future__ division""" raise NotImplementedError @abstractmethod + def __truediv__(self, other): + """self / other with __future__ division. + + Should promote to float when necessary. + """ + raise NotImplementedError + + @abstractmethod + def __rtruediv__(self, other): + """other / self with __future__ division""" + raise NotImplementedError + + @abstractmethod def __pow__(self, exponent): """self**exponent; should promote to float or complex when necessary.""" raise NotImplementedError Index: Lib/test/test_rational.py =================================================================== --- Lib/test/test_rational.py (revision 0) +++ Lib/test/test_rational.py (revision 0) @@ -0,0 +1,229 @@ +"""Tests for Lib/rational.py.""" + +from test.test_support import run_unittest, verbose +import math +import rational +import unittest +R = rational.Rational + +def _components(r): + return (r.numerator, r.denominator) + +class RationalTest(unittest.TestCase): + + def assertTypedEquals(self, expected, actual): + """Asserts that both the types and values are the same.""" + self.assertEquals(type(expected), type(actual)) + self.assertEquals(expected, actual) + + def assertRaisesMessage(self, exc_type, message, + callable, *args, **kwargs): + """Asserts that callable(*args, **kwargs) raises exc_type(message).""" + try: + callable(*args, **kwargs) + except exc_type, e: + self.assertEquals(message, str(e)) + else: + self.fail("%s not raised" % exc_type.__name__) + + def testInit(self): + self.assertEquals((-1, 1), _components(R(-1, 1))) + self.assertEquals((-1, 1), _components(R(1, -1))) + self.assertEquals((1, 1), _components(R(-2, -2))) + self.assertEquals((1, 2), _components(R(5, 10))) + self.assertEquals((7, 15), _components(R(7, 15))) + self.assertEquals((10**23, 1), _components(R(10**23))) + + try: + R(12, 0) + self.fail("R(12, 0) failed to raise ZeroDivisionError") + except ZeroDivisionError as e: + self.assertEquals("Rational(12, 0)", str(e)) + + self.assertRaises(TypeError, R, 1.5) + self.assertRaises(TypeError, R, 1.5 + 3j) + + def testFromFloat(self): + self.assertRaisesMessage( + TypeError, "Rational.from_float() only takes floats, not 3 (int)", + R.from_float, 3) + + self.assertEquals((0, 1), _components(R.from_float(-0.0))) + self.assertEquals((10, 1), _components(R.from_float(10.0))) + self.assertEquals((-5, 2), _components(R.from_float(-2.5))) + self.assertEquals((99999999999999991611392, 1), + _components(R.from_float(1e23))) + self.assertEquals(float(10**23), float(R.from_float(1e23))) + self.assertEquals((3602879701896397, 1125899906842624), + _components(R.from_float(3.2))) + self.assertEquals(3.2, float(R.from_float(3.2))) + + inf = 1e1000 + nan = inf - inf + self.assertRaisesMessage( + TypeError, "Cannot convert inf to Rational.", + R.from_float, inf) + self.assertRaisesMessage( + TypeError, "Cannot convert -inf to Rational.", + R.from_float, -inf) + self.assertRaisesMessage( + TypeError, "Cannot convert nan to Rational.", + R.from_float, nan) + + def testConversions(self): + self.assertTypedEquals(-1, trunc(R(-11, 10))) + self.assertTypedEquals(-2, R(-11, 10).__floor__()) + self.assertTypedEquals(-1, R(-11, 10).__ceil__()) + self.assertTypedEquals(-1, R(-10, 10).__ceil__()) + + self.assertTypedEquals(0, R(-1, 10).__round__()) + self.assertTypedEquals(0, R(-5, 10).__round__()) + self.assertTypedEquals(-2, R(-15, 10).__round__()) + self.assertTypedEquals(-1, R(-7, 10).__round__()) + + self.assertEquals(False, bool(R(0, 1))) + self.assertEquals(True, bool(R(3, 2))) + self.assertTypedEquals(0.1, float(R(1, 10))) + self.assertTypedEquals(0.1+0j, complex(R(1,10))) + + def testRound(self): + self.assertTypedEquals(R(-200), R(-150).__round__(-2)) + self.assertTypedEquals(R(-200), R(-250).__round__(-2)) + self.assertTypedEquals(R(30), R(26).__round__(-1)) + self.assertTypedEquals(R(-2, 10), R(-15, 100).__round__(1)) + self.assertTypedEquals(R(-2, 10), R(-25, 100).__round__(1)) + + + def testArithmetic(self): + self.assertEquals(R(1, 2), R(1, 10) + R(2, 5)) + self.assertEquals(R(-3, 10), R(1, 10) - R(2, 5)) + self.assertEquals(R(1, 25), R(1, 10) * R(2, 5)) + self.assertEquals(R(1, 4), R(1, 10) / R(2, 5)) + self.assertTypedEquals(2, R(9, 10) // R(2, 5)) + self.assertTypedEquals(10**23, R(10**23, 1) // R(1)) + self.assertEquals(R(2, 3), R(-7, 3) % R(3, 2)) + self.assertEquals(R(8, 27), R(2, 3) ** R(3)) + self.assertEquals(R(27, 8), R(2, 3) ** R(-3)) + self.assertTypedEquals(2.0, R(4) ** R(1, 2)) + # Will return 1j in 3.0: + self.assertRaises(ValueError, pow, R(-1), R(1, 2)) + + def testMixedArithmetic(self): + self.assertTypedEquals(R(11, 10), R(1, 10) + 1) + self.assertTypedEquals(1.1, R(1, 10) + 1.0) + self.assertTypedEquals(1.1 + 0j, R(1, 10) + (1.0 + 0j)) + self.assertTypedEquals(R(11, 10), 1 + R(1, 10)) + self.assertTypedEquals(1.1, 1.0 + R(1, 10)) + self.assertTypedEquals(1.1 + 0j, (1.0 + 0j) + R(1, 10)) + + self.assertTypedEquals(R(-9, 10), R(1, 10) - 1) + self.assertTypedEquals(-0.9, R(1, 10) - 1.0) + self.assertTypedEquals(-0.9 + 0j, R(1, 10) - (1.0 + 0j)) + self.assertTypedEquals(R(9, 10), 1 - R(1, 10)) + self.assertTypedEquals(0.9, 1.0 - R(1, 10)) + self.assertTypedEquals(0.9 + 0j, (1.0 + 0j) - R(1, 10)) + + self.assertTypedEquals(R(1, 10), R(1, 10) * 1) + self.assertTypedEquals(0.1, R(1, 10) * 1.0) + self.assertTypedEquals(0.1 + 0j, R(1, 10) * (1.0 + 0j)) + self.assertTypedEquals(R(1, 10), 1 * R(1, 10)) + self.assertTypedEquals(0.1, 1.0 * R(1, 10)) + self.assertTypedEquals(0.1 + 0j, (1.0 + 0j) * R(1, 10)) + + self.assertTypedEquals(R(1, 10), R(1, 10) / 1) + self.assertTypedEquals(0.1, R(1, 10) / 1.0) + self.assertTypedEquals(0.1 + 0j, R(1, 10) / (1.0 + 0j)) + self.assertTypedEquals(R(10, 1), 1 / R(1, 10)) + self.assertTypedEquals(10.0, 1.0 / R(1, 10)) + self.assertTypedEquals(10.0 + 0j, (1.0 + 0j) / R(1, 10)) + + self.assertTypedEquals(0, R(1, 10) // 1) + self.assertTypedEquals(0.0, R(1, 10) // 1.0) + self.assertTypedEquals(10, 1 // R(1, 10)) + self.assertTypedEquals(10**23, 10**22 // R(1, 10)) + self.assertTypedEquals(10.0, 1.0 // R(1, 10)) + + self.assertTypedEquals(R(1, 10), R(1, 10) % 1) + self.assertTypedEquals(0.1, R(1, 10) % 1.0) + self.assertTypedEquals(R(0, 1), 1 % R(1, 10)) + self.assertTypedEquals(0.0, 1.0 % R(1, 10)) + + # No need for divmod since we don't override it. + + # ** has more interesting conversion rules. + self.assertTypedEquals(R(100, 1), R(1, 10) ** -2) + self.assertTypedEquals(R(100, 1), R(10, 1) ** 2) + self.assertTypedEquals(0.1, R(1, 10) ** 1.0) + self.assertTypedEquals(0.1 + 0j, R(1, 10) ** (1.0 + 0j)) + self.assertTypedEquals(4 , 2 ** R(2, 1)) + # Will return 1j in 3.0: + self.assertRaises(ValueError, pow, (-1), R(1, 2)) + self.assertTypedEquals(R(1, 4) , 2 ** R(-2, 1)) + self.assertTypedEquals(2.0 , 4 ** R(1, 2)) + self.assertTypedEquals(0.25, 2.0 ** R(-2, 1)) + self.assertTypedEquals(1.0 + 0j, (1.0 + 0j) ** R(1, 10)) + + def testComparisons(self): + self.assertTrue(R(1, 2) < R(2, 3)) + self.assertFalse(R(1, 2) < R(1, 2)) + self.assertTrue(R(1, 2) <= R(2, 3)) + self.assertTrue(R(1, 2) <= R(1, 2)) + self.assertFalse(R(2, 3) <= R(1, 2)) + self.assertTrue(R(1, 2) == R(1, 2)) + self.assertFalse(R(1, 2) == R(1, 3)) + + def testMixedLess(self): + self.assertTrue(2 < R(5, 2)) + self.assertFalse(2 < R(4, 2)) + self.assertTrue(R(5, 2) < 3) + self.assertFalse(R(4, 2) < 2) + + self.assertTrue(R(1, 2) < 0.6) + self.assertFalse(R(1, 2) < 0.4) + self.assertTrue(0.4 < R(1, 2)) + self.assertFalse(0.5 < R(1, 2)) + + def testMixedLessEqual(self): + self.assertTrue(0.5 <= R(1, 2)) + self.assertFalse(0.6 <= R(1, 2)) + self.assertTrue(R(1, 2) <= 0.5) + self.assertFalse(R(1, 2) <= 0.4) + self.assertTrue(2 <= R(4, 2)) + self.assertFalse(2 <= R(3, 2)) + self.assertTrue(R(4, 2) <= 2) + self.assertFalse(R(5, 2) <= 2) + + def testBigFloatComparisons(self): + """The first test demonstrates why these are important.""" + self.assertFalse(1e23 < float(R(trunc(1e23) + 1))) + self.assertTrue(1e23 < R(trunc(1e23) + 1)) + self.assertFalse(1e23 <= R(trunc(1e23) - 1)) + self.assertTrue(1e23 > R(trunc(1e23) - 1)) + self.assertFalse(1e23 >= R(trunc(1e23) + 1)) + + def testMixedEqual(self): + self.assertTrue(0.5 == R(1, 2)) + self.assertFalse(0.6 == R(1, 2)) + # Because 10**23 can't be represented exactly as a float: + self.assertFalse(R(10**23) == float(10**23)) + self.assertTrue(R(1, 2) == 0.5) + self.assertFalse(R(1, 2) == 0.4) + self.assertTrue(2 == R(4, 2)) + self.assertFalse(2 == R(3, 2)) + self.assertTrue(R(4, 2) == 2) + self.assertFalse(R(5, 2) == 2) + + def testStringification(self): + self.assertEquals("rational.Rational(7,3)", repr(R(7, 3))) + self.assertEquals("(7/3)", str(R(7, 3))) + self.assertEquals("7", str(R(7, 1))) + + def testHash(self): + self.assertEquals(hash(2.5), hash(R(5, 2))) + self.assertNotEquals(hash(float(10**23)), hash(R(10**23))) + +def test_main(): + run_unittest(RationalTest) + +if __name__ == '__main__': + test_main()